There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((x + 1){e}^{3})}{(2{x}^{2} + 2x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{xe^{3}}{(2x^{2} + 2x)} + \frac{e^{3}}{(2x^{2} + 2x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{xe^{3}}{(2x^{2} + 2x)} + \frac{e^{3}}{(2x^{2} + 2x)}\right)}{dx}\\=&(\frac{-(2*2x + 2)}{(2x^{2} + 2x)^{2}})xe^{3} + \frac{e^{3}}{(2x^{2} + 2x)} + \frac{x*3e^{2}*0}{(2x^{2} + 2x)} + (\frac{-(2*2x + 2)}{(2x^{2} + 2x)^{2}})e^{3} + \frac{3e^{2}*0}{(2x^{2} + 2x)}\\=&\frac{-4x^{2}e^{3}}{(2x^{2} + 2x)^{2}} - \frac{6xe^{3}}{(2x^{2} + 2x)^{2}} + \frac{e^{3}}{(2x^{2} + 2x)} - \frac{2e^{3}}{(2x^{2} + 2x)^{2}}\\ \end{split}\end{equation} \]

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